Abstract
Efficient energy transfer often occurs between oscillation modes in a resonator when they are tuned to internal resonance. We design the eigenfrequencies of two vibrational modes of an electromechanical resonator to be close to a ratio of and demonstrate that the energy supplied to the upper mode can be controllably transferred to the lower mode. With the lower mode vibrating with a period tripled that of the upper mode, the discrete time-translation symmetry imposed by the periodic drive is broken. The lower mode settles into one of three stable period-tripled states with different phases. This channel for energy transfer from the upper mode can be turned on or off without changing system parameters. When the upper mode itself becomes multistable under strong resonant or parametric drive, additional sets of coexisting period-tripled states emerge in the lower mode. In the latter case, we measure a total of six coexisting vibration states with identical amplitude but phases differing by . Excitation of coexisting states with three different phases could open new opportunities in designing mechanical memory based on ternary logic. Coupled resonators with period-tripled states can also be used to model complex interacting systems with spin equal to one.
- Received 22 September 2021
- Accepted 1 June 2022
DOI:https://doi.org/10.1103/PhysRevX.12.031003
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
From celestial bodies to ecological systems, nonlinear interactions allow oscillatory modes of drastically different frequencies to couple. For nanoscale resonators, there has been much progress in developing schemes to control the energy transfer from one mode to another, thus allowing the modes to be optimized as sensors of weak signals, stable clocks for timekeeping, or versatile memory elements for storage and computation. Here, we demonstrate experimentally a new way to manipulate the energy transfer for two coupled modes in an electromechanical resonator.
We demonstrate that energy supplied to the higher mode of the resonator can be controllably transferred to a lower mode to excite stable vibrations with a period triple that of the higher mode. The vibrations in the lower mode are tristable: They take on one of three possible values of phase. The energy transfer can be turned on and off by applying an appropriate perturbation to the lower mode. When the upper mode itself has multiple oscillation states, the energy transfer leads to multiple sets of coexisting period-tripled states in the lower mode.
Our work opens new opportunities for using coexisting oscillation states in applications that go beyond the conventional binary (zeros and ones) representation of information. Coupled resonators with three period-tripled states can be used to model complex interacting systems with a spin equal to 1. They can also find applications in ternary logic systems, which may offer advantages in terms of power density and information density over binary systems.
